Nadia is 4 times as old as Vanessa. Twelve years ago, Nadia was 7 times as old as Vanessa. How old is Nadia now?
Explanation: We can use the given information to write down two equations that describe the ages of Nadia and Vanessa. Let Nadia's current age be $n$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $n = 4v$ Twelve years ago, Nadia was $n - 12$ years old, and Vanessa was $v - 12$ years old. The information in the second sentence can be expressed in the following equation: $n - 12 = 7(v - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $n$ , it might be easiest to solve our first equation for $v$ and substitute it into our second equation. Solving our first equation for $v$ , we get: $v = n / 4$ . Substituting this into our second equation, we get: $n - 12 = 7($ $(n / 4)$ $- 12)$ which combines the information about $n$ from both of our original equations. Simplifying the right side of this equation, we get: $n - 12 = \dfrac{7}{4} n - 84$ Solving for $n$ , we get: $\dfrac{3}{4} n = 72$ $n = \dfrac{4}{3} \cdot 72 = 96$.